Having won their first two UEFA Champions League fixtures, Diego Simeone's side kicked off full of confidence and were almost sure of the points before 20 minutes had been played. García tapped in Filipe Luis's pass to give the visitors the lead before Costa doubled their advantage with a superb individual effort and rounded off a fine evening's work with his second and Atlético's third early in the second half.

Austria had begun in positive fashion in an unfamiliar gold and black third kit but were soon on the back foot as Juanfran came forward. The Atlético right-back unleashed an early swerving drive which Heinz Lindner did well to palm behind for a corner.

The Rojiblancos' first goal was not long in coming, Koke's cute slide-rule pass down the left channel in the eighth minute springing the offside trap. Luis drew the goalkeeper before squaring for García to roll into an empty net.

Further setbacks followed for Austria, first when top scorer Marko Stankovic suffered a recurrence of his calf injury and had to be withdrawn and then when Costa cut through their defence. Picking up possession on the halfway line the forward turned, advanced, beat two defenders and coolly slipped the ball past the left leg of a helpless Lindner to make it 2-0 with less than a quarter of the match gone.

It had been one-way traffic yet suddenly Atlético started to drop deeper and Austria dominated the rest of the first period. Their best chance came when Philipp Hosiner found himself unmarked at the far post but the striker blasted a close-range volley against the crossbar.

If Nenad Bjelica's Austrian champions had left themselves with plenty of work to do, they took their spirited display from the end of the first half into the second, Florian Mader nearly bringing renewed hope with a long-range drive that flew just over.

Group G's bottom club going into this game, Austria's increased attacking urgency left them vulnerable to Atlético's slick incisive attacks – and so it proved eight minutes after the restart. Costa received a pass from substitute Emiliano Insúa inside the penalty area and turned to beat Lindner again.

Atlético now hold a five-point cushion at the top of the group, having won all three fixtures, and will look to make it four when the teams reconvene in Spain on matchday four. Austria remain in fourth position with a single point.

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